Math & Science ⇒ Sparse block-Toeplitz matrix

[petri-j-vaisanen]

Hi,
I did some searching but couldn't find anything on the subject, so my question is that how would you define sparse block-Toeplitz matrix? Here's my attempt:

Code: Select all

\documentclass{article}
\usepackage{mathtools}
\usepackage{amsfonts}

\begin{document}
\begin{equation} \label{tMat1}
\mathbf{T} = 
 \begin{bmatrix}
  \mathbf{V}_{A} & \mathbf{0} & \cdots & \mathbf{0} \\
  \mathbf{V}_{B} & \mathbf{V}_{A} & & \vdots \\
  \mathbf{0} & \mathbf{V}_{B} & \ddots & \mathbf{0} \\
  \vdots & \mathbf{0} & \ddots & \mathbf{V}_{A} \\
  \mathbf{0} & \mathbf{0} & \cdots & \mathbf{V}_{B} 
 \end{bmatrix} \\
 \in \mathbb{C}^{NQ+W-1 \times NK}
\end{equation}
, where it is assumed that $W \leq L$ and that
\begin{equation} \label{vMtx1}
\mathbf{V} = \left[ \mathbf{V}_{A} \mathbf{V}_{B} \right]^{T}  = \left[  \mathbf{b}^{(1)} \mathbf{b}^{(2)} \ldots \mathbf{b}^{(K)} \right] \in \mathbb{C}^{Q+W-1 \times K}
\end{equation}
\end{document}

but I would like to use that \mathbf{V} only in the matrix \mathbf{T}, somehow "overlapping" each others? Any ideas?


Edit:
I used the PGF/TikZ package to create columns of the Toeplitz matrix as boxes and put those inside equation environment. I'll post the code later.

[petri-j-vaisanen]

Here's very quick code using tikz-package for block matrix:

Code: Select all

\documentclass{article}
\usepackage{mathtools}
\usepackage{amsfonts}
\usepackage{tikz}

\begin{document}
\begin{equation}
\begin{bmatrix}
\begin{tikzpicture}[line width=1pt]
  \def\rectanglepath{-- ++(0cm,2.5cm) -- ++(0.75cm,0cm) -- ++(0cm,-2.5cm) -- cycle}

  \draw (0.0,0.0) \rectanglepath;
  \draw (1*0.75,-0.1) \rectanglepath;
  \draw (3*0.75,-0.4) \rectanglepath;
  \draw (0.75/2,2.5/2) node {$\mathbf{V}$};
  \draw (0.75/2+0.75,2.5/2-0.1) node {$\mathbf{V}$};
  \draw (0.75/2+3*0.75,2.5/2-0.4) node {$\mathbf{V}$};
  \draw (0.75/2+2*0.75,2.5/2-0.3) node {$\ddots$};
 
\end{tikzpicture}
\end{bmatrix}
\end{equation}

\end{document}